The character moves normally, however the frames are such that the added movement of the sprite on top of the "move by" value makes them stutter and glide a little. The walk cycle is perfect in the sprite editor because that doesn't have the added movement.
What if a person had a character that had a different walk motion though, something that meant you didn't want them to be in constant motion when walking, like the zombie you mention? The added movement again, would mess this up somewhat.
So, is it possible to move the player character sprite solely with the "move by" values? That's all I'm asking. This would be perfect as it would allow you to move the character at whatever speed you wanted, and you could stagger their movement (if you wanted) by not "moving" some of the frames in the sprite. If it can't be done then fine, I can get around this, but I would prefer not to.